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Parameter Adaptation Algorithms — Stochastic Environment

  • I. D. Landau
  • R. Lozano
  • M. M’Saad
Part of the Communications and Control Engineering book series (CCE)

Abstract

Consider the estimation of a plant model disturbed by a stochastic process which can be represented by:
$$\begin{array}{*{20}{c}} {y(t + 1) = - {{A}^{*}}({{q}^{{ - 1}}})y(t) + {{B}^{*}}({{q}^{{ - 1}}})u(t) + w(t + 1)} \\ { = {{\theta }^{T}}\phi (t) + w(t + 1)} \\ \end{array}$$
(4.1.1)
where u is the input, y is the output, w is a the zero mean stationary stochastic disturbance with finite moments and:
$$ {\theta ^T} = \left[ {{a_1} \ldots {a_{{n_A},}}{b_1} \ldots {b_{{n_B}}}} \right] $$
(4.1.2)
$$ {\phi ^T}\left( t \right) = \left[ { - y\left( t \right) \ldots - y\left( {t - {n_A} + 1} \right),u\left( t \right) \ldots u\left( {t - {n_B} + 1} \right)} \right] $$
(4.1.3)
Let’s consider an equation error type adjustable predictor (like in RLS).

Keywords

Output Error Adaptation Algorithm Stochastic Environment Stochastic Disturbance Adaptation Error 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag London 1998

Authors and Affiliations

  • I. D. Landau
    • 1
  • R. Lozano
    • 2
  • M. M’Saad
    • 3
  1. 1.GR-Automatique EnsiegSt Martin d’HèresFrance
  2. 2.CNRS, HEUDIASYCCompiegne Technological UniversityCompiegne CedexFrance
  3. 3.Caen University, ISMRACaen CedexFrance

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